Chapter 3.4, Problem 41PPS

To determine

To conjecture: The effect of increase in value of divisor on the quotient.

Answer to Problem 41PPS

The value of the divisor increases, the quotient decreases.

Explanation of Solution

Given information.

The model at the left shows: $\frac{3}{4}÷\frac{1}{2}$

The model at the right shows: $\frac{3}{4}÷\frac{1}{4}$

 

In the first model:

The divisor is: $\frac{1}{2}$

The quotient is: $1\frac{1}{2}$

In the second model:

The divisor is $\frac{1}{4}$

The quotient is: 3

It is seen that as the value of the divisor increases, the quotient decreases.

Consider the following cases:

(1) $\frac{3}{4}÷\frac{1}{16}$

  $=\frac{3}{4}\cdot \frac{16}{1}\left[\text{Multiply by the reciprocal}\frac{16}{1}\right]$

  $=12$  [Cancel the common factors]

(2)

  $\frac{3}{4}÷\frac{1}{12}$

  $=\frac{3}{4}\cdot \frac{12}{1}\left[\text{Multiply by the reciprocal}\frac{12}{1}\right]$

  $=9$  [ Cancel the common factors]

(3)

  $\frac{3}{4}÷\frac{1}{8}$

  $=\frac{3}{4}\cdot \frac{8}{1}\left[\text{Multiply by the reciprocal}\frac{8}{1}\right]$

  $=6$  [Cancel the common factors]

Thus, as the value of the divisor increases, the quotient decreases.